A water heater contains 54 gal of water. How many kilowatt hours of energy are necessary to heat the water in the water heater by 25° C

Answer 1

q = mC∆T

q = heat = ?

m = mass of water = see below

C = specific heat of water = 4.184 J/gº

∆T = change in temperature of the water = 25º

Because we have C in units of J/gº, we'll need to change 54 gal to grams. We'll assume a density of 1 g/ml for water, and a conversion factor of 3785 mls per gallon.

Thus, we have...

54 gallons x 3785 mls / gallon x 1 g / ml = 204,390 g of water

q = (204,390 g)(4.184 J/gº)(25) = 21,379,194 Joules = 21.4 MJ (megajoules)

It turns out that 1 MJ equals 0.278 kilowatt hours (kWh), so our conversion becomes...

21.4 MJ x 0.278 kWh / MJ = 5.95 kWh (answer)